Using preserved river channels, we have been able to constrain the size of floods in Martian rivers more than 3.5 billion years ago. That information tells us only so much about the climate, however, because we do not know how often the floods occurred. To get a better sense of the amount of water that rained or snowed on Mars, we need to measure the amount of erosion that has taken place.
These measurements are challenging, because most of the ancient river valleys are partly filled by wind-blown sand. Width is measured using pictures from visible and infrared cameras. Valley depth is given by laser shots from the Mars Orbiter Laser Altimeter (MOLA) or from U.S. or European stereo image datasets. Stereo imaging works by photographing the same area from two somewhat different angles, like the depth perception in our eyes. We also use MOLA topography to measure the amount of infilling and rim erosion in impact craters, whose initial depth and rim height depend on crater diameter.
Figure: Valley networks in the Martian highlands, colored to show topography (warm colors are high elevations, cool colors are low).